In 1968, Robert Brehme1 wrote a carefully crafted paper on “The Advantage of Teaching Relativity with Four-Vectors.” In his abstract he points out that “the emphasis on relativistic mass is both undeserved and misleading.” Our approach is to find the best way to teach introductory physics in a way that includes modern physics. We have found that by starting with special relativity in the first week of the course, we establish a background we can use to introduce modern physics topics as we go along. While we agree that the four-vector formalism for relativity is elegant, it is clearly inappropriate in a physics course where we have not even discussed the concept of a coordinate system. Instead, we base all our discussion on the principle of relativity itself,2 which we feel may be a more basic concept than Minkowski's four vectors.
REFERENCES
This is described in the “Lack of simultaneity” paper in Ref. 2.
This result was derived by Feynman in Volume I Lecture 16, page 16–6. We have a slightly simpler derivation.